Integrated supply chain of supplier and retailer for stochastic demand

This article deals with a two-stage supply chain comprising of the retailer and the supplier in which demand of the end customers follows news-vendor type demand. The setup costs, purchasing and procurement costs are dependent on lot sizes. The mathematical models for continuous and discrete variables of the chain are analyzed mathematically to maximize the expected average profits of individual and the collaborating systems. As our study suggests that collaborating system is always better than the decentralized system for known distribution cases, we also optimize the joint profit of the retailer and the supplier for a distribution free case which is implemented for unknown distribution. Finally, numerical examples of the demand patterns are illustrated to justify the proposed model. The punctual research directions from the proposed model are also provided in the conclusion section.